Question
D) Simplify. Express your answer using positive exponents. \( \frac{2 c^{6} \cdot 7 c}{7 c^{7}} \)
Ask by Lynch Nguyen. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified result is \(2\).
Solution
1. Multiply the factors in the numerator:
\[
2c^6 \cdot 7c = 14c^{6+1} = 14c^7.
\]
2. Write the fraction:
\[
\frac{14c^7}{7c^7}.
\]
3. Simplify by canceling common factors. The \( c^7 \) cancels:
\[
\frac{14}{7} = 2.
\]
The simplified result is \(2\).
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Simplify this solution Extra Insights
First, let's simplify the expression step by step. The \(7 c\) in the numerator and the \(7 c^{7}\) in the denominator cancel out the \(7\) and reduce the power of \(c\). This leaves us with: \[ \frac{2 c^{6} \cdot 1}{c^{6}} = 2 c^{6 - 7} = 2 c^{-1} \] Now, using positive exponents, we rewrite \(c^{-1}\) as \(\frac{1}{c}\). Therefore, the final simplified expression is: \[ \frac{2}{c} \]
